Geometric Methods in Bio-Medical Image Processing

ISBN-13: 9783540432166 / Angielski / Twarda / 2002 / 147 str.

Ravikanth Malladi

Opis

Itgivesmegreatpleasuretoeditthisbook. Thegenesisofthisbookgoes backtotheconferenceheldattheUniversityofBolognainJune1999, on collaborativeworkbetweentheUniversityofCaliforniaatBerkeleyandthe UniversityofBologna. Theoriginalideawastoinvitesomespeakersatthe conferencetosubmitarticlestothebook. Thescopeofthebookwaslater- hancedand, inthepresentform, itisacompilationofsomeoftherecentwork usinggeometricpartialdi?erentialequationsandthelevelsetmethodology inmedicalandbiomedicalimageanalysis. Thesynopsisofthebookisasfollows: Inthe?rstchapter, R. Malladi andJ. A. Sethianpointtotheoriginsoftheuseoflevelsetmethodsand geometricPDEsforsegmentation, andpresentfastmethodsforshapes- mentationinbothmedicalandbiomedicalimageapplications. InChapter 2, C. OrtizdeSolorzano, R. Malladi, andS. J. Lockettdescribeabodyof workthatwasdoneoverthepastcoupleofyearsattheLawrenceBerkeley NationalLaboratoryonapplicationsoflevelsetmethodsinthestudyand understandingofconfocalmicroscopeimagery. TheworkinChapter3byA. Sarti, C. Lamberti, andR. Malladiaddressestheproblemofunderstanding di?culttimevaryingechocardiographicimagery. Thisworkpresentsvarious levelsetmodelsthataredesignedto?tavarietyofimagingsituations, i. e. timevarying2D,3D, andtimevarying3D. InChapter4, L. VeseandT. F. Chanpresentasegmentationmodelwithoutedgesandalsoshowextensions totheMumford-Shahmodel. Thismodelisparticularlypowerfulincertain applicationswhencomparisonsbetweennormalandabnormalsubjectsis- quired. Next, inChapter5, A. EladandR. Kimmelusethefastmarching methodontriangulateddomaintobuildatechniquetounfoldthecortexand mapitontoasphere. Thistechniqueismotivatedinpartbynewadvances infMRIbasedneuroimaging. InChapter6, T. DeschampsandL. D. Cohen presentaminimalpathbasedmethodofgroupingconnectedcomponentsand showcleverapplicationsinvesseldetectionin3Dmedicaldata. Finally, in Chapter7, A. Sarti, K. Mikula, F. Sgallari, andC. Lamberti, describean- linearmodelfor?lteringtimevarying3Dmedicaldataandshowimpressive resultsinbothultrasoundandechoimages. IoweadebtofgratitudetoClaudioLambertiandAlessandroSartifor invitingmetoBologna, andlogisticalsupportfortheconference. Ithank thecontributingauthorsfortheirenthusiasmand?exibility, theSpringer mathematicseditorMartinPetersforhisoptimismandpatience, andJ. A. Sethianforhisunfailingsupport, goodhumor, andguidancethroughthe years. Berkeley, California R. Malladi October,2001 Contents 1 FastMethodsforShapeExtractioninMedicaland BiomedicalImaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. Malladi, J. A. Sethian 1. 1Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2TheFastMarchingMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3ShapeRecoveryfromMedicalImages. . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 AGeometricModelforImageAnalysisinCytology. . . . . . . 19 C. OrtizdeSolorzano, R. Malladi, S. J. Lockett 2. 1Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2. 2GeometricModelforImageAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2. 3SegmentationofNuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. 4SegmentationofNuclei

Recenzje

From the reviews:

R. Malladi (ed.)

Geometric Methods in Bio-Medical Image Processing

"This is an excellent monograph on geometric methods in biomedical image processing. I strongly recommend this book to visualization experts in mathematics, computer science and bio-medical applications and to research students on above topics."-JOURNAL OF COMPUTATIONAL METHODS IN APPLIED MATHEMATICS

"This book is based on the conference held at the University of Bologna at June 1999. ... The book gives a good review on some of the traditional applications in medical imagery (CT, MR, Ultrasound). ... This is an excellent monograph on geometric methods in biomedical image processing. I strongly recommend this book to visualization experts in mathematics, computer science and bio-medical applications and to research students on the above topics." (T. E. Simos, Journal of Computational Methods in Sciences and Engineering, Vol. 3 (2), 2003)

Spis treści

1 Fast Methods for Shape Extraction in Medical and Biomedical Imaging.- 1.1 Introduction.- 1.2 The Fast Marching Method.- 1.3 Shape Recovery from Medical Images.- 1.4 Results.- References.- 2 A Geometric Model for Image Analysis in Cytology.- 2.1 Introduction.- 2.2 Geometric Model for Image Analysis.- 2.3 Segmentation of Nuclei.- 2.4 Segmentation of Nuclei and Cells Using Membrane-Related Protein Markers.- 2.5 Conclusions.- References.- 3 Level Set Models for Analysis of 2D and 3D Echocardiographic Data.- 3.1 Introduction.- 3.2 The Geometric Evolution Equation.- 3.3 The Shock-Type Filtering.- 3.4 Shape Extraction.- 3.5 2D Echocardiography.- 3.6 2D + time Echocardiography.- 3.7 3D Echocardiography.- 3.8 3D + time Echocardiography.- 3.9 Conclusions.- References.- 4 Active Contour and Segmentation Models using Geometric PDE’s for Medical Imaging.- 4.1 Introduction.- 4.2 Description of the Models.- 4.3 Applications to Bio-Medical Images.- 4.4 Concluding Remarks.- References.- 5 Spherical Flattening of the Cortex Surface.- 5.1 Introduction.- 5.2 Fast Marching Method on Triangulated Domains.- 5.3 Multi-Dimensional Scaling.- 5.4 Cortex Unfolding.- 5.5 Conclusions.- References.- 6 Grouping Connected Components using Minimal Path Techniques.- 6.1 Introduction.- 6.2 Minimal Paths in 2D and 3D.- 6.3 Finding Contours from a Set of Connected Components Rk.- 6.4 Finding a Set of Paths in a 3D Image.- 6.5 Conclusion.- References.- 7 Nonlinear Multiscale Analysis Models for Filtering of 3D + Time Biomedical Images.- 7.1 Introduction.- 7.2 Nonlinear Diffusion Equations for Processing of 2D and 3D Still*Images.- 7.3 Space-Time Filtering Nonlinear Diffusion Equations.- 7.4 Numerical Algorithm.- 7.5 Discussion on Numerical Experiments.- 7.6 Preconditioning and Solving of Linear Systems.- References.- Appendix. Color Plates.